I have a large Abelia right outside my kitchen door. It has so much nectar that in the early morning it drips like rain onto my kitchen steps.
I asked our palynologist about it when he visited our bee club. Dr. Arnold said that honeybees can't get nectar from Abelia directly - like the bumblebee does. The bumblebee dives headfirst into the abelia and sucks the nectar but it is also hard for the bumblebee to do this. So often the Bumblebee slits the flower near the base to have more convenient access to the nectar.
At our bee meeting Dr. Arnold suggested that Abelia had an extrafloral nectary but upon research and a later email from him, it turns out that it is the slit that is being used, not an extrafloral nectary.
You may see honeybees hanging onto the base of an abelia blossom, getting nectar sideways, as it were. But because it isn't easy for them to get the Abelia nectar, it will not be a dominant pollen or nectar in your honey.http://beekeeperlinda.blogspot.com/2008/06/honeybee-botany-and-dr-paul-arnold.html
Linda T in Atlanta